Basic Math Examples

$5^{- 1} - 10^{- 2}$

Step 1

Simplify each term.

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Step 1.1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{5} - 10^{- 2}$

Step 1.2

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{5} - \frac{1}{10^{2}}$

Step 1.3

Raise $10$ to the power of $2$ .

$\frac{1}{5} - \frac{1}{100}$

Step 2

To write $\frac{1}{5}$ as a fraction with a common denominator, multiply by $\frac{20}{20}$ .

$\frac{1}{5} \cdot \frac{20}{20} - \frac{1}{100}$

Step 3

Write each expression with a common denominator of $100$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{1}{5}$ by $\frac{20}{20}$ .

$\frac{20}{5 \cdot 20} - \frac{1}{100}$

Step 3.2

Multiply $5$ by $20$ .

$\frac{20}{100} - \frac{1}{100}$

Step 4

Combine the numerators over the common denominator.

$\frac{20 - 1}{100}$

Step 5

Subtract $1$ from $20$ .

$\frac{19}{100}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{19}{100}$

Decimal Form:

$0.19$